1. Field of the Invention
The invention relates to wagering games, such as those typically played in a casino or online, and more specifically to wagering games played by placing bets on an outcome derived from a random event.
2. Related Art
Wagering on outcomes derived from a random event has been and remains a common source of entertainment. In fact, the development of gambling techniques led to the beginning of modern statistics. See, for example, Galilei's work, Sopra le Scoperte dei Dadi (1620), which was first published in 1718. A number of casino table games, such as craps, roulette, and keno are based on the placing of bets or wagers on randomized events. Similarly, a number of electronic casino games are based on placing bets on randomized events.
In general, game players wager on a variety of randomized outcomes. Outcomes that have a lesser probability of occurring usually have a higher payout-to-wager ratio than outcomes that have a greater probability of occurring. A number of wagering games are complex in that the games provide for a great number of wagers. For example, craps and roulette have a great number of wager options. For many gamblers, having more betting options increases the entertainment value of a wagering game. However, by increasing wager options, the game may become too complex for a novice gambler that prefers simpler wagering games. For example, in a coin-toss game there are only two outcomes to wager on, heads or tails, and both outcomes have the same probability of occurring. Such a game may be enjoyable for a novice or a gambler that is in the mood for a simpler game. Some games provide both complex and simple wagers. For example, in roulette, a player may place a simple bet on red or black. On the other hand, a player may place a more complex wager by betting on several numbers on a roulette board. The complex and simple options for wagering in roulette derive from the various events that may occur from spinning a roulette wheel.
Another apparatus well-suited for generating random events to wager on is a die or dice. The most commonly used die for wagering is the six-sided die like that showing all six sides in two dimension, i.e., unfolded, in FIG. 1. For example, a player can roll a die and wager on one of six outcomes. Another game that could come out of rolling one die is wagering on odd or even results, in other words, wagering on two possible outcomes of a single die roll. Another game that could come out of rolling one die is wagering on a roll of one or two (low roll), three or four (middle roll), or five or six (high roll), in other words, wagering on three possible outcomes of a single die roll. From one roll of a die, a casino could thus provide three concurrent games; one based upon randomizations in a range of 1 to 6, one based upon randomizations in the range of 1 to 2, and the last based upon randomizations in the range of 1 to 3.
A number of wagering games use more than one die. By increasing the number of dice, the possible outcomes in a roll of the dice increase. For example, when rolling one die there are six possible outcomes and rolling two dice there are thirty-six possible outcomes. However, for all 36 possibilities to be determined, the dice used must be distinguished from each other, for example, by using one red die and one blue die. If the roll is, say, a 1 on the red die and a 2 on the blue die, this can be distinguished from a 1 on the blue die and a 2 on the red die.
If the dice used are indistinguishable from each other, and if both dice are thrown at the same time, there is no way to distinguish between these example rolls. Thus, using indistinguishable dice, from the thirty-six possible outcomes, there are twenty-one distinct outcomes. (A list of such outcomes is shown below in Table 8.) So the roll of two indistinguishable dice provides a randomization of elements in a set of 21 identifiers. In addition, the value of each die can be summed together, resulting in another randomization value ranging from 2 to 12. The basis of craps, the most popular casino dice game in the world, is wagering on these twenty-one distinct outcomes and on the 11 sums resulting from the rolling of two indistinguishable dice. For many people, craps is a complex game; however, a two dice roll can also be suited for simpler games. For example, one could bet on low (2-6) or high (8-12) outcomes of a two dice roll.
When rolling three distinguishable dice, 216 possible rolls result. If the dice are non-distinguishable, 56 distinct rolls result, and the sums range from 3 to 18. The basis of popular casino games, including Ricochet, is wagering on one of the 56 distinct outcomes and on the 16 sums resulting. (A list of such outcomes is shown in Table 10.)
People have created many games using three six-sided dice. For example, a dice game described in U.S. Pat. No. 5,879,006 (Bowling) makes use of three indistinguishable dice, all rolled at the same time. Furthermore, people have created games employing three six-sided dice in which there are various physical or procedural differences, providing ways to distinguish the dice from one another, creating more than the 56 distinct results. Sic Bo is a 3-dice game, but actually uses two indistinguishable dice and one die colored differently from the other 2. So, Sic Bo is not based upon 56 distinct rolls, it is based upon 126 distinct rolls. In U.S. Pat. No. 6,209,874 (Jones), the game disclosed uses three dice, each having a different color, providing 216 possible outcomes. U.S. Pat. No. 6,893,019 (Gaygen) provides a three dice roll outcome, as well as a two dice roll outcome, and a one die roll outcome, all in the same roll. This game and many others like it boast the capability of providing multiple outcome ranges from a given roll.
Similarly, in U.S. Pat. No. 6,378,869 (Hedge and Hedge), two dice are thrown, and then the one die; a procedural way of providing the same numerical distinction of U.S. Pat. No. 6,893,019, thus also providing multiple outcome ranges from a given roll. U.S. Pat. No. 4,743,025 (Gramera) discloses a set of three distinguishable six-sided dice, where each of the two hundred and sixteen possible numerical combinations of the roll are visually differentiated by varying the numeral formats on each die. Hence, 216 possible outcomes can be deciphered from such a three dice roll. Gramera describes the need for multiple outcome ranges from a given roll as follows: “Since the three dice in a set of conventional dice are of identical color, it is virtually impossible for game participants to visually differentiate each of the two-hundred-sixteen possible rolled combinations that display the sixteen numerical sums, ranging in values from three through eighteen. Without the ability to visually differentiate each of the two-hundred-sixteen possible numerical combinations of three dice, all current dice related games using a conventional set of 3 dice of one color, incorporating various game boards, playing cards or a combination thereof, are limited to only the normally expected sixteen visually discernable numerical scores, each of which turns up with varying odds. As a result, a great number of games currently available, utilize either several six-sided dice or dice with more than six sides, to compensate for the scoring limitation that is clearly evident when either a set of two or three conventional six-sided dies are used in various games of chance.” (Gramera at Column 2, lines 4-22.)
Other examples can be found also attempting to provide additional wagering and outcome ranges from a given roll. Specifically, to provide the two-dice roll outcome range from a three dice roll, all of the prior art examples are implemented by providing a means to distinguish between the dice thrown. What has never before been done is to provide additional wagering and outcome ranges using three indistinguishable dice, all thrown at once. It is widely believed that this is not possible, as Gramera states. (Supra.)
U.S. Pat. No. 4,743,025 (Scheb et al.) discloses another game using 3 distinguishable dice. Scheb et al. describes as disclosing U.S. Pat. No. 6,234,482, a multiple dice game wherein players' wager relate to the outcome of a roll of three dice without differentiation of three dice. Wagers are limited to wagers regarding the total of the three dice and/or the existence of two or three identical numbers being rolled.
Therefore, a method and apparatus is needed in the gaming art to provide additional randomization ranges, and in particular a method and apparatus to facilitate multiple games to all be played concurrently against the same randomization event, e.g., a dice roll, wheel spin, etc. These games should have the ability to greatly range in variety and complexity. The literature sites many examples of the need for simple games, as well as more complex games to captivate the interest of novice and experienced players alike. By providing a wide range of game selections based upon the various mappings, it is possible that players of all ranges of experience can enjoy playing games of their choice, all together at the same time, against the same randomization event, e.g., a live roll of dice, spin of a prize wheel or selection of a player card from a deck.